The Rangers scored three goals on six shots in a span of 4:08 in the first period.
Kreider scored with a net-front deflection of Vladimir Tarasenko's shot at 6:13 to give New York a 1-0 lead. Kakko scored with a low shot from the right circle 1:28 later, making it 2-0 at 7:41. Motte flung a low shot off the left-wing half wall into the near side of the net for a 3-0 lead at 10:21.
"Direct hockey, closing on guys, physical, getting in battles, winning battles, advancing pucks, that was a strong game for us for the majority," Kreider said. "The thing on a lot of the goals was attacking the net, attacking the net."
Alex Killorn scored a power-play goal 19 seconds later at 10:40 with a net-front deflection of Mikhail Sergachev's shot to cut it to 3-1.
Raddysh, playing his 17th NHL game, made it 3-2 with a shot from the point at 7:10 of the second period. The goal was originally credited to Brandon Hagel but changed to Raddysh.
"We battled back," Lightning defenseman Victor Hedman said. "Maybe a little bit of an exhale after clinching a playoff spot, and we can't really move because [it will be hard] to get to second place. We can't let bad habits creep into our game, but we showed we battled back and played the way we wanted."
Motte scored his second of the game 15 seconds later at 7:25 after making a move around Sergachev to give New York a 4-2 lead.